The statement which correctly describes the shaded region for the inequality is
Further explanation:
In the question it is given that the inequality is .
The equation corresponding to the inequality is
.
The equation represents a line and the inequality
represents the region which lies either above or below the line
.
Transform the equation in its slope intercept form as
, where
represents the slope of the line and
represents the
-intercept.
-intercept is the point at which the line intersects the
-axis.
In order to convert the equation in its slope intercept form add
to equation
.
Now, divide the above equation by .
Compare the above final equation with the general form of the slope intercept form .
It is observed that the value of is
and the value of
is
.
This implies that the -intercept of the line is
so, it can be said that the line passes through the point
.
To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute for
in
.
This implies that the line passes through the point .
Now plot the points and
in the Cartesian plane and join the points to obtain the graph of the line
.
Figure shows the graph of the equation
.
Now to obtain the region of the inequality consider any point which lies below the line
.
Consider to check if it satisfies the inequality
.
Substitute and
in
.
The above result obtain is not true as is not greater than
so, the point
does not satisfies the inequality
.
Now consider to check if it satisfies the inequality
.
Substitute and
in the inequality
.
The result obtain is true as is greater than
so, the point
satisfies the inequality
.
The point lies above the line so, the region for the inequality
is the region above the line
.
The region the for the inequality does not include the points on the line
because in the given inequality the inequality sign used is
.
Figure shows the region for the inequality
.
Therefore, the statement which correctly describes the shaded region for the inequality is
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear inequality
Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.
